I'm just curious and was wondering:

MAX1620/MAX1621 states it can use a range of voltage between 3 to 5.5 volts.
DS1390 states it can do 2.97 to 5.5 volts.
16LF818 states it can do up to 2 to 5.5 volts.

So with maybe a little parts massaging you could use a 3.7 battery. Though pricey and needing a connection could you use two of these or something similar to get the life you desire? http://www.newark.com/dantona-indust...mah/dp/14N3902 They are thinner than a 9 volt battery so two could fit where one 9 volt battery currently resides.